conditional risk

It can be interpreted as a sequence of conditional risk measures.

The expected loss (conditional risk) associated with taking action is given by:

A mapping is a conditional risk measure if it has the following properties:

The dynamic superhedging price has conditional risk measures of the form:

A conditional risk measure is said to be regular if for any and then where is the indicator function on .

A risk measure can be thought of as a conditional risk measure on the trivial sigma algebra.

The financial interpretation of this states that the conditional risk at some future node (i.e. ) only depends on the possible states from that node.

In financial mathematics, a conditional risk measure is a random variable of the financial risk (particularly the downside risk) as if measured at some point in the future.

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